An easy completeness proof for the modal µ-calculus on finite trees

Authors:
Balder ten Cate;Gaëlle Fontaine
Affiliations:
University of California, Santa Cruz;ILLC, Universiteit van Amsterdam
Venue:
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Year:
2010

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Abstract

We give a complete axiomatization for the modal μ-calculus on finite trees. While the completeness of our axiomatization already follows from a more powerful result by Igor Walukiewicz in [11], our proof is easier and uses very different tools, inspired from model theory. We show that our approach generalizes to certain axiomatic extensions, and to the extension of the μ-calculus with graded modalities. We hope that the method might be helpful for other completeness proofs as well.